/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 Explain each of the following co... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 47

Explain each of the following concepts. You may use graphs to illustrate each concept. a. Perfect positive linear correlation b. Perfect negative linear correlation c. Strong positive linear correlation d. Strong negative linear correlation e. Weak positive linear correlation f. Weak negative linear correlation g. No linear correlation

Short Answer

Expert verified
The various types of linear correlations - perfect positive, perfect negative, strong positive, strong negative, weak positive, weak negative, and no correlation - depict the relationships between two variables, representing how changes in one variable relate to the changes in another. They can be illustrated by respective graphs showing trends in data points.

Step by step solution

01

Perfect Positive Linear Correlation

In a perfect positive linear correlation, all the points lie exactly on a straight line going upwards. This means that as one variable increases, the other also increases at a consistent rate. A graph illustrating this would feature a straight, upward-sloping line with all points on it.
02

Perfect Negative Linear Correlation

In a perfect negative linear correlation, all points lie exactly on a line going downwards. This means that as one variable increases, the other decreases at a consistent rate. A graph illustrating this would feature a straight, downward-sloping line with all points on it.
03

Strong Positive Linear Correlation

A strong positive linear correlation means that as one variable increases, the other also increases and the points tend to be close to a straight line going upwards. Although they're not perfectly aligned, they still form a visible upward trend. A graph portraying this would feature an upward-sloping line with points clustered around it.
04

Strong Negative Linear Correlation

A strong negative linear correlation means that as one variable increases, the other decreases and the points tend to remain close to a straight line going downwards. Without being perfectly aligned, they still form a distinct downward trend. A graph illustrating this would feature a downward-sloping line with points clustering around it.
05

Weak Positive Linear Correlation

A weak positive linear correlation is defined by a vague upward trend. As one variable increases, the other generally increases as well, but the points aren't clustered closely to an upward-sloping line 鈥� they're rather spread out. A graph portraying this would depict an upward-sloping line with points widely dispersed around it.
06

Weak Negative Linear Correlation

A weak negative linear correlation represents a vaguely downward trend. The points aren't tightly clustered around a downward-sloping line 鈥� instead, they're rather diffused. As one variable increases, the other generally decreases, but the relationship is quite weak and data points are wide-spread. This would be illustrated by a downward-sloping line with points spread scattered around.
07

No Linear Correlation

Finally, no linear correlation is represented when there is no recognizable pattern or trend between two variables. Regardless of changes in one variable, the other seems to change randomly. The points on the graph are widely scattered, showing no specific direction upwards or downwards. It might be depicted as a cloud of points with no distinct pattern.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain the meaning of independent and dependent variables for a regression model.

A population data set produced the following information. $$ \begin{aligned} &N=250, \quad \Sigma x=9880, \quad \Sigma y=1456, \quad \sum x y=85,080, \\ &\Sigma x^{2}=485,870, \text { and } \Sigma y^{2}=135,675 \end{aligned} $$ Find the linear correlation coefficient \(\rho\).

Two variables \(x\) and \(y\) have a negative linear relationship. Explain what happens to the value of \(y\) when \(x\) increases. Give one example of a negative relationship between two variables.

The recommended air pressure in a basketball is between 7 and 9 pounds per square inch (psi). When dropped from a height of 6 feet, a properly inflated basketball should bounce upward between 52 and 56 inches . The basketball coach at a local high school purchased 10 new basketballs for the upcoming season, inflated the balls to pressures between 7 and 9 psi, and performed the bounce test mentioned above. The data obtained are given in the following table. $$ \begin{array}{l|rrrrrrrrrr} \hline \text { Pressure (psi) } & 7.8 & 8.1 & 8.3 & 7.4 & 8.9 & 7.2 & 8.6 & 7.5 & 8.1 & 8.5 \\ \hline \begin{array}{l} \text { Bounce height } \\ \text { (inches) } \end{array} & 54.154 .3 & 55.2 & 53.3 & 55.4 & 52.2 & 55.7 & 54.6 & 54.8 & 55.3 \\ \hline \end{array} $$ a. With the pressure as an independent variable and bounce height as a dependent variable, compute \(\mathrm{SS}_{x}, \mathrm{SS}_{y y}\), and \(\mathrm{SS}_{x y-}\) b. Find the least squares regression line. c. Interpret the meaning of the values of \(a\) and \(b\) calculated in part b. d. Calculate \(r\) and \(r^{2}\) and explain what they mean. e. Compute the standard deviation of errors. f. Predict the bounce height of a basketball for \(x=8.0\). g. Construct a \(98 \%\) confidence interval for \(B\). h. Test at a \(5 \%\) significance level whether \(B\) is different from zero. i. Using \(a=.05\), can you conclude that \(\rho\) is different from zero?

An economist is studying the relationship between the incomes of fathers and their sons or daughters. Let \(x\) be the annual income of a 30 -year-old person and let \(y\) be the annual income of that person's father at age 30 years, adjusted for inflation. A random sample of 300 thirty-year-olds and their fathers yields a linear correlation coefficient of \(.60\) between \(x\) and \(y .\) A friend of yours, who has read about this research, asks you several questions, such as: Does the positive value of the correlation coefficient suggest that the 30 -year-olds tend to earn more than their fathers? Does the correlation coefficient reveal anything at all about the difference between the incomes of 30 -year-olds and their fathers? If not, what other information would we need from this study? What does the correlation coefficient tell us about the relationship between the two variables in this example? Write a short note to your friend answering these questions.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.